# Longest subarray with equal number of ones and zeros

## Problem

You are given an array of 1's and 0's only. Find the longest subarray which contains equal number of 1's and 0's.

## Solution

We will keep a running sum of "no of ones minus no of zeros" for each index of the array. For any two indices, if the running sum is equal, that means there are equal number of ones and zeros between these two indices. We will store the running sum in an array such that it acts like a hash map where key is the running sum and value is the leftmost index of that running sum to appear. The running sum can vary from -n to +n. So we need an array of length 2*n+1. So for any index we can check whether this sum has occurred before and if yes what is the left most index for it. We can do this in O(1) time by maintaining the array. So at any index we can find the longest equal subarray till that point. We will compare it with a maximum value and update the maximum accordingly. So the overall complexity for the process is O(n)

## Code

public class MaxSubarrayEqualOnesZeros { public static void main(String[] args) { int[] arr = { 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0 }; printMaxSubarray(arr); } private static void printMaxSubarray(int[] arr) { Integer[] diffMap = new Integer[arr.length * 2 + 1]; diffMap[arr.length] = -1; int sum = 0; int maxLength = 0; int maxStart = -1; int maxEnd = -1; for (int i = 0; i < arr.length; ++i) { if (arr[i] == 0) sum -= 1; else sum += 1; Integer prevIndex = diffMap[arr.length + sum]; if (prevIndex == null) diffMap[arr.length + sum] = i; else { if (i - prevIndex > maxLength) { maxLength = i - prevIndex; maxStart = prevIndex + 1; maxEnd = i; } } } System.out.println("indices (" + maxStart + "," + maxEnd + ")"); System.out.println("length=" + maxLength); } }